Math 2.0

Subjects

54 General topology

See MSC 54 on zbMATH Open.

NameTagKindMSC
Closure is the set of limits of sequences003QP7A8HGstatement54E35
Finite intersection property00BWV5CKCFstatement54D30
Closed map00FSJTXPJMconcept54C10
Compact set00R0X1WGPXdefinition54D30
Second-countable space00RE1R4W7Ndefinition54D70
Topological embedding00ZG9Y9TR4concept54C25
Totally disconnected space01CYW8S04Ddefinition54D05
Urysohn's lemma01EY3VR7ZDstatement54D15
Triangle inequality for a metric01M6CW9VM6statement54E35
Isolated point01PKQYTTMTdefinition54A05
Cantor set is closed01VT24J1SDstatement54F65
Open set01ZQQDCERPdefinition54A05
Totally bounded set020Q06TYYHconcept54E35
Open set02BH3MCBQBconcept54A05
Open balls form a basis of the metric topology02EEX96DFSstatement54E35
Isometry02HPP5VCZHconcept54E40
Isometries are injective02J4G4J4TJstatement54E40
Topological property02SMVGC690concept54A05
Closure is closed02TZDKG50Qstatement54A05
Arzelà–Ascoli theorem0381S8Z5P0statement54C35
Regular space03HMJASQBQconcept54D15
Second-countable space03PPNCM9GGconcept54D70
Lebesgue number lemma040CFNJEAPstatement54E45
Continuous bijection from a compact space to a Hausdorff space is a homeomorphism0430ETCMKDstatement54D30
Product metric044D4AQV8Vdefinition54E35
Open cover049PXYHW1Tconcept54D30
Separation axioms04J4BYB0XEconcept54D10
Product topology on an arbitrary product04S9HX3GAPdefinition54B10
Compact iff complete and totally bounded054Q5PW5GXstatement54E45
Boundary05D5EGMFYVconcept54A05
Closed ball05DSV40EB9definition54E35
T1 space05GQJXBP3Fdefinition54D10
Homeomorphism05GZ11PWRYdefinition54C05
Composition of continuous maps is continuous05NK26G0DRstatement54C05
Metric space063W5JMY85definition54E35
Inclusion of a subspace is continuous065J822CKNstatement54B05
Closed subsets of compact sets are compact066HW6D9A7statement54D30
Closure in a metric space068P0P32DWstatement54E35
Diameter of a set0692CGQF00definition54E35
Heine–Cantor theorem06B8BNJCD6statement54E45
Basis of a topology06EX0FHBTFdefinition54A05
Convergence of a sequence in a metric space06JYPJ4WHHdefinition54E35
Completion of a metric space06RW4RKWH7concept54E50
Comparison of topologies072J68M6HXconcept54A10
Continuity at a point of a topological space07N7W5C29Xdefinition54C05
Heine–Borel theorem07PFYV65MBstatement54E45
T0 space07SG12TQH3concept54D10
Distance from a point to a set07TXYYVYZRdefinition54E35
Isometry0878DN3WCSdefinition54E40
Complete metric space08EWT7J0SCdefinition54E50
Topological embedding08SVRVHJNYdefinition54C25
Comparison of topologies08XFJJ8EYWdefinition54A10
Convergence of a sequence in a metric space090AA928Y7concept54E35
Metrizable space091GJ3FYD7concept54E35
Intermediate value theorem for connected spaces098C0KZZAPstatement54D05
Open sets characterised by neighbourhoods09CJ00H3NWstatement54A05
Closed sets contain their limits09GQ3ZTQJ9statement54E35
Completeness of the space of bounded continuous functions09GRCZVR5Estatement54C35
Metrizable space09KDHB82SGdefinition54E35
Finite intersection of open sets is open09NDE9V7X1statement54E35
Bounded set09QSZVVM26concept54E35
Subbasis09S8DV34Y0concept54A05
Equivalent metrics09V3NASXNDconcept54E35
Intersection of closed sets is closed09YMV8H4X5statement54E35
Product of compact sets is compact09ZKE5XQ74statement54D30
Isolated point0A1YXSKB48concept54A05
Open sets of a metric space0A26X79RTBstatement54E35
Pseudometric space0A3HJX3KTFconcept54E35
Metric topology0A6YRNZB2Rdefinition54E35
Baire category theorem0A7KGAYHGVstatement54E52
Metrizable spaces are normal0AD0BZ49DWstatement54E35
Normal space0AJ646N339definition54D15
Product metric0AYV6VGKF5concept54E35
Open balls are open0B2305GNAZstatement54E35
Continuity via closed sets0B8GPXFSP7statement54C05
Cofinite topology0B906ZBTMZexample54A05
Connected subsets of the real line are intervals0B9ZQFMQNVstatement54D05
Dense set0BSJSX7ME2concept54A05
Box topology0BWJTRE3X3concept54B10
Cantor set0BXNDZFQMEexample54F65
Complete metric space0BY52JW6NKconcept54E50
Interior0C38S0KMJKdefinition54A05
Sequential compactness0CARW59WD2definition54D30
Subbasis0CHR35YNJQdefinition54A05
Topological space0CNQXVBHCXdefinition54A05
First-countable space0CP5NDD21Cconcept54D70
Topological space0CQHFPGJ45concept54A05
Box topology0CTM1EHG9Pdefinition54B10
Dense set0D198GPMTJdefinition54A05
A set is closed iff it equals its closure0D2W7FS52Tstatement54A05
Baire space0D5KR33H7Xdefinition54E52
Subspace topology0D5YHQGDJYdefinition54B05
Limits are unique in Hausdorff spaces0D8T984XEEstatement54D10
Connected space0D939CMME7definition54D05
Open ball0DC3MPR7C9definition54E35
Closure0DRKT1QJR7definition54A05
Limit point0E3X7TXS67concept54A05
Epsilon-delta continuity in metric spaces0EKGKY5TGHstatement54E35
Continuous image of a connected set is connected0EPD87YVG8statement54D05
Locally compact space0EQMWQ4WMJdefinition54D45
Cantor's intersection theorem0EZBG8SKJMstatement54D30
Closed subsets of complete spaces are complete0FBXJZX3MKstatement54E50
Locally compact space0FE2SB8WVJconcept54D45
Universal property of the quotient topology0FF2FJ8CH2statement54B15
Epsilon-delta uniform continuity0FHSDCQACYstatement54E40
Meagre set0FQPYAY9PJdefinition54E52
Sequential compactness0FRMJH3CY7concept54D30
Completion of a metric space0G4J7Z7WPJdefinition54E50
Closed set0G5AV9Q4RRdefinition54A05
Product topology0GBG8B49AAconcept54B10
Separable space0GKJ78948Vdefinition54D65
One-point compactification0GWN3CMRK8concept54D35
Pseudometric space0H3W614GECdefinition54E35
Interior is the largest open subset0HAZEFH137statement54A05
Limit point0HBQC2GJXTdefinition54A05
Union of open sets is open0HEF46RPEKstatement54E35
First-countable space0HG11FW8MJdefinition54D70
Regular space0JF9KW2TXBdefinition54D15
Boundary0JJ9J1XZ8Gdefinition54A05
Tychonoff's theorem0JTRSJKCFBstatement54D30
Path-connected space0K0GE6BCYWdefinition54D05
Topologist's sine curve0K3T4A659Rcounterexample54G20
Complement of an open set is closed0K67Q60Z8Pstatement54A05
Compactness and sequential compactness agree in metric spaces0K8SGQSV7Gstatement54E45
Continuous image of a compact set is compact0K9AAJ8G51statement54D30
Continuity at a point0KRMJRDRZTconcept54C05
Nowhere dense set0KSM23SN3Hdefinition54E52
Diameter of a set0KW3PN547Kconcept54E35
Usual metric on the real line0KXJTZSW9Bexample54E35
Universal property of the product topology0M6W4XNST6statement54B10
Epsilon characterisation of Cauchy sequences0MCK8K2D7Zstatement54E35
One-point compactification0MM45BT6HCdefinition54D35
Compact Hausdorff spaces are normal0MQQQ5NA2Sstatement54D30
Equicontinuity0MW2WXTHMCdefinition54C35
Hausdorff space0MXB4CKHFWdefinition54D10
Open connected subsets of R^n are path-connected0MXN7AFBPEstatement54D05
Compact subsets of a Hausdorff space are closed0MYFJVMN7Mstatement54D30
Completeness via Cauchy sequences0N1ZWFJDN5statement54E50
Basis of a topology0NA0732YAGconcept54A05
Discrete metric0NA4FK7B8Sexample54E35
Epsilon-net characterisation of total boundedness0NMGJJ19HDstatement54E35
Quotient topology0NQ1H2X495concept54B15
Connected components are closed0NRT0E2QT2statement54D05
Normal space0NSR9V8TEDconcept54D15
Open cover0NVPNC12JYdefinition54D30
T1 space0NW6CH38YRconcept54D10
Closed map0NYZ2M45G9definition54C10
Compactness via open covers0P6PMJB4MAstatement54D30
Bounded set0P953MG05Edefinition54E35
Metric spaces are Hausdorff0P9DCDES73statement54E35
Projections are continuous0PM88Z9W4Mstatement54B10
Interior is open0PNWCM559Pstatement54A05
Closed ball0Q0H13G8ZBconcept54E35
Subspace metric0QBYFZV91Pconcept54E35
Closure0QEAJB91GZconcept54A05
Compact space0QPHW703PVdefinition54D30
Homeomorphism0QT00PB5G2concept54C05
Connected set0R37DFJKFWdefinition54D05
T0 space0R3B7DX55Jdefinition54D10
Compact set0R6EWFKRCFconcept54D30
Compact subsets of a metric space are bounded0R7BTEWCJ2statement54E45
Totally disconnected space0RJSBR9GW1concept54D05
Proper metric space0RN765S7DHconcept54E45
Cantor set is homeomorphic to the space of binary sequences0RQ8DHHR8Vstatement54F65
Interior0RZH6W98HKconcept54A05
Hausdorff space0S1FJ8VEX9concept54D10
Discrete topology0S2TEHX4E1example54A05
Path component0SB9FNZECGdefinition54D05
Closure is the smallest closed superset0SHC6Z304Zstatement54A05
Connected set0SPE8WNWFVconcept54D05
Open map0SQ2PC596Ydefinition54C10
Continuous map of topological spaces0SY9ECQ19Qdefinition54C05
Subspace metric0T2WYDTRP2definition54E35
Compact space0TVJZYB6SHconcept54D30
Equivalent metrics0TWQ5PRKWSdefinition54E35
Connected space0V032VWTHDconcept54D05
Continuous real function on a compact set attains its bounds0V4DET59NWstatement54C30
Quotient topology0V8046R0P9definition54B15
Continuous map0VGFHTM75Yconcept54C05
Continuity is equivalent to sequential continuity in metric spaces0VGPKZ8MRKstatement54E35
Metric space0VKD1TP7F3concept54E35
Nowhere dense set0VQYCCQVJ5concept54E52
Isometric isomorphism0VRD8GC5BMdefinition54E40
Sup metric on R^n0VTAXQEWQDexample54E35
Complete subspaces are closed0W41XG4W60statement54E50
Path-connected space0WB6DH499Tconcept54D05
Totally bounded set0WE5BBHGM6definition54E35
Circle as a quotient of the real line0WH1GVBJNHexample54B15
Distance from a point to a set0WQ19TJV24concept54E35
Subspace topology0WS9P12FQRconcept54B05
Countable intersection of dense open sets is dense0X2T63GFQQstatement54E52
Path component0X3EG7Y65Tconcept54D05
Tietze extension theorem0X52TNMTCJstatement54C20
Meagre set0XGCZ4GDZ6concept54E52
Indiscrete topology0XJ02JBD6Sexample54A05
Equicontinuity0XN66MZN0Yconcept54C35
Open map0YCG648KDDconcept54C10
Open ball0YE5868HZBconcept54E35
Continuity via open sets0YF82GBTNDstatement54E35
Closed balls are closed0YS40B38JDstatement54E35
Metric topology0YVKNB7V5Fconcept54E35
Separable space0Z2P41SVDPconcept54D65
Proper metric space0Z4V98VN5Edefinition54E45
Product topology0Z57EC6YX3definition54B10
Closed set0ZCK8DQYN1concept54A05
Baire space0ZH5AJ2ED7concept54E52
Path-connected spaces are connected0ZMT1GP4KMstatement54D05
Isometric isomorphism0ZXSF2YQV2concept54E40